We prove the scattering for a defocusing nonlinear Schrödinger equation with a sum of two repulsive potentials with strictly convex level surfaces, thus providing a scattering result in a trapped setting similar to the exterior of two strictly convex obstacles.
Nous montrons la diffusion pour une équation de Schrödinger non linéaire défocalisante avec une somme de deux potentiels répulsifs dont les surfaces de niveau sont strictement convexes. Il s’agit d’un résultat dans une géométrie captante similaire à l’extérieur de deux obstacles strictement convexes.
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Keywords: nonlinear Schrödinger equation, scattering, trapped trajectories, Morawetz estimates, concentration-compactness/rigidity
Mot clés : équation de Schrödinger non linéaire, diffusion, trajectoires captées, estimées de Morawetz, concentration-compacité/rigidité
Lafontaine, David 1
@article{AIF_2020__70_5_1847_0, author = {Lafontaine, David}, title = {Scattering for {NLS} with a sum of two repulsive potentials}, journal = {Annales de l'Institut Fourier}, pages = {1847--1869}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {70}, number = {5}, year = {2020}, doi = {10.5802/aif.3385}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.3385/} }
TY - JOUR AU - Lafontaine, David TI - Scattering for NLS with a sum of two repulsive potentials JO - Annales de l'Institut Fourier PY - 2020 SP - 1847 EP - 1869 VL - 70 IS - 5 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.3385/ DO - 10.5802/aif.3385 LA - en ID - AIF_2020__70_5_1847_0 ER -
%0 Journal Article %A Lafontaine, David %T Scattering for NLS with a sum of two repulsive potentials %J Annales de l'Institut Fourier %D 2020 %P 1847-1869 %V 70 %N 5 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.3385/ %R 10.5802/aif.3385 %G en %F AIF_2020__70_5_1847_0
Lafontaine, David. Scattering for NLS with a sum of two repulsive potentials. Annales de l'Institut Fourier, Volume 70 (2020) no. 5, pp. 1847-1869. doi : 10.5802/aif.3385. https://aif.centre-mersenne.org/articles/10.5802/aif.3385/
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